23.4. Geometric Interpretation

Try these first

1. 1.

   Are the vectors (1,2) and (2,4) linearly independent?

   Hint

   Check if one can be expressed as a multiple of the other.

2. 2.

   Is the set of vectors (3, 1) and (1, -4) linearly independent?

   Hint

   Consider their direction in the 2D plane.

3. 3.

   Two vectors are linearly independent if they are:

   • A) Collinear
   • B) Non-collinear
   • C) Opposite

   Hint

   Think about their direction in the plane.

4. 4.

   In R³, three vectors are linearly independent when they are:

   • True
   • False

   Hint

   Consider the relationship of three planes.

5. 5.

   Prove whether the following set of vectors: (2, 3), (4, 6), and (1, 1) is linearly independent or dependent.

   Hint

   Use the definition of linear independence to check combinations.

6. 6.

   Design an example of three vectors in R³ which are linearly independent and explain why.

   Hint

   Check their arrangement in space.